I'd guess what you are seeing is actually a difference in the AR coating, and probably not a difference in the crystal itself. Mineral and sapphire are very hard to tell apart visually. Mineral crystals, viewed from the edge, appear a bit green (like a pane of window glass), and sapphire crystals appear a bit pink - but it is very subtle.
Sapphire crystals are basically the same material as sapphire stones, except the sapphires for watch crystals are lab-grown. Actually, I think sapphires and rubies are the same chemical composition, except for impurities in the material that give them a red or blue color.